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framed elliptic curve

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Definition

Over the complex numbers, a framed elliptic curve is an elliptic curve equipped with an ordered basis {a,b}\{a,b\} of the homology of the curve such that the intersection number aba\cdot b is 1 (e.g. Hain 08, def. 1.13).

The standard construction of the moduli stack of elliptic curves is in fact via the orbifold quotient of the space of framed elliptic curves acted on by the modular group.

A framing on an elliptic curve is in a way the extreme case of a level structure on an elliptic curve.

A framed elliptic curve is in particular naturally a framed manifold (a framed surface).

References

  • Richard Hain, Lectures on Moduli Spaces of Elliptic Curves (arXiv:0812.1803)

Last revised on September 8, 2014 at 06:32:38. See the history of this page for a list of all contributions to it.